Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:

import java.io.*;
import java.util.*;

//    O(N*M)

public class Main {
    public static void main (String[] args) throws java.lang.Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(st.nextToken()),
            m = Integer.parseInt(st.nextToken());
        int[][] board = new int[n+1][m+1];
        int[][] board2 = new int[n+1][m+1];
        for (int i=1 ; i<=n ; i++) {
            st = new StringTokenizer(br.readLine());
            for (int j=1 ; j<=m ; j++) {
                board[i][j] = Integer.parseInt(st.nextToken());
                board2[i][j] = board[i][j];
            }
        }
        
        int count1 = 0;
        int count2 = 0;
        int[] rows1 = new int[n+1];
        int[] cols1 = new int[m+1];
        int[] rows2 = new int[n+1];
        int[] cols2 = new int[m+1];
        for (int i=1 ; i<=n ; i++) {
            int min = 501;
            for (int j=1 ; j<=m ; j++) {
                if (board[i][j] == 0) {
                    min = 501;
                    break;
                }
                if (board[i][j]<min) min = board[i][j];
            }
            if (min == 501) continue;
            rows1[i] = min;
            count1 += min;
            for (int j=1 ; j<=m ; j++) board[i][j] -= min;
        }
        for (int i=1 ; i<=m ; i++) {
            int min = 501;
            for (int j=1 ; j<=n ; j++) {
                if(board[j][i] == 0) {
                    min = 501;
                    break;
                }
                if (board[j][i]<min) min = board[j][i];
            }
            if (min == 501) continue;
            cols1[i] = min;
            count1 += min;
            for (int j=1 ; j<=n ; j++) board[j][i] -= min;
        }
        board = board2;
        for (int i=1 ; i<=m ; i++) {
            int min = 501;
            for (int j=1 ; j<=n ; j++) {
                if(board[j][i] == 0) {
                    min = 501;
                    break;
                }
                if (board[j][i]<min) min = board[j][i];
            }
            if (min == 501) continue;
            cols2[i] = min;
            count2 += min;
            for (int j=1 ; j<=n ; j++) board[j][i] -= min;
        }
        for (int i=1 ; i<=n ; i++) {
            int min = 501;
            for (int j=1 ; j<=m ; j++) {
                if (board[i][j] == 0) {
                    min = 501;
                    break;
                }
                if (board[i][j]<min) min = board[i][j];
            }
            if (min == 501) continue;
            rows2[i] = min;
            count2 += min;
            for (int j=1 ; j<=m ; j++) board[i][j] -= min;
        }
        //    System.out.println(count1 + " " + count2);
        int count = count1;
        int[] rows = rows1,
            cols = cols1;
        if (count1>count2) {
            count = count2;
            rows = rows2;
            cols = cols2;
        } 
        
        for (int i=1 ; i<=n ; i++) {
            for (int j=1 ; j<=m ; j++) {
                if (board[i][j] != 0) {
                    System.out.println(-1);
                    return;
                }
            }
        }
        System.out.println(count);
        for (int i=1 ; i<=n ; i++) {
            if (rows[i] == 0) continue;
            for (int j=0 ; j<rows[i] ; j++) System.out.println("row " + i);
        }
        for (int i=1 ; i<=m ; i++) {
            if (cols[i] == 0) continue;
            for (int j=0 ; j<cols[i] ; j++) {
                System.out.println("col " + i);
            }
        }
    }
}